Ocean waves are "emergent phenomena" that arise out of the complexity of forces active in a large body of water. Photo by Chris Potter.
The conclusions … depend on ideas that must first be well comprehended
and which are now novel to the large majority of readers and unfamiliar
to all. But those who care to brace themselves to a sustained
effort need not feel much regret that the road to be traveled over is indirect,
and does not admit of being mapped beforehand in a way they can clearly
understand. It is full of interest on its own. It familiarizes us with
curious laws of chance that apply to a vast diversity of social subjects.
This part of inquiry may be said to run along a road on a high level, that
affords wide views in unexpected directions, and from which easy descents
may be made to totally different goals to those we have now to reach. I
have a great subject to write upon, but feel keenly my literary
incapacity to make it easily intelligible without sacrificing
accuracy and thoroughness. (Pp. 2-3)
Order in Apparent Chaos … I know
of scarcely anything so apt to impress the imagination as the wonderful
form of cosmic order expressed by the ‘Law of Frequency of Error’.
The law would have been personified by the Greeks and deified,
if they had known of it. It reigns with serenity and in complete self-effacement
amidst the wildest confusion. The huger the mob, and the greater the apparent
anarchy, the more perfect is its sway. It is the supreme law of
Unreason. Whenever a large sample of chaotic elements are taken
in hand and marshalled in the order of their magnitude, an unsuspected
and most beautiful form of regularity proves to have been latent all along.
The tops of the marshalled row form a flowing curve of invariable proportions;
and each element, as it is sorted into place, finds, as it were, a pre-ordained
niche, accurately adapted to fit it. If the measurement at any two specified
Grades in the row are known, those that will be found at every other Grade,
except towards the extreme ends, can be predicted in the way already explained,
and with much precision.
Problems in the Law of Error… All
the properties of the Law of Frequency of Error can be expressed in terms
of Q, or the Prob: Error, just as those of a circle can
be expressed in terms of its radius. The visible Schemes are not,
however, to be removed too soon from our imagination. It is always well
to retain a clear geometric view of the facts when we are dealing with
statistical problems, which abound with dangerous pitfalls, easily overlooked
by the unwary, while they are cantering gaily along upon their arithmetic. The
Laws of Error are beautiful in themselves and exceedingly fascinating to
inquirers, owing to the thoroughness and simplicity with which they deal
with masses of materials that appear at first sight to be entanglements
on the largest scale, and of hopelessly confused description…
Galton, Francis. Natural Inheritance, Macmillan and Co. London, 1889, pp. 66-67.
